A state of emergency has been declared in the city and neighbouring Selwyn District and the military has been deployed to help firefighters.
At least 11 homes have already been destroyed and smoke has spread across the city.
On Tuesday, a decorated army pilot was killed when his helicopter crashed.
Cpl David Steven Askin had been awarded for his bravery while deployed in Afghanistan, for helping save the lives of guests during a hotel siege in Kabul in 2011.
`Don`t leave it too late`
The Port Hills fire broke out in two separate places on Monday in the dry hills south of Christchurch, before merging into one blaze which now covers abut 1,800ha.
More than 130 firefighters have been deployed, along with 14 helicopters and three aircraft brought in from across the South Island.
A total of 400 homes were evacuated by police, but hundreds of other people have also chosen to leave the area.
Police Snr Sgt Ash Tabb warned people that fires can change direction and move quickly, giving little time to escape.
"If you`re worried, don`t leave it too late - it`s better to be safe than sorry."
One man told New Zealand`s Stuff website that he watched his home burn down from a distance.
"I can`t believe it`s just caught on fire after it survived the night," said Henry Reese.
A Facebook group has been set up by local residents who are offering rooms or properties for people who have left their homes.
Prime Minister Bill English arrived in Christchurch on Thursday morning and viewed the fire from the air.
He said it was "contained but not controlled", but that the local community "knows how to stick together when things are difficult".
With smoke spreading across the city, the council has issued a warning to residents to see a doctor if they experience breathing difficulties.
Christchurch fires: Homes destroyed and residents evacuated
16 February 2017
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Hundreds of homes have been evacuated in the New Zealand city of Christchurch as a huge wildfire rages on its outskirts.
